Assumption REF  also assumes that \(G_t\)  has full row rank, which is a common constraint qualification to ensure the uniqueness of the dual solution.
By the compactness of \(\mathcal {X}\) , we have \(G_tG_t^T\succeq \gamma _{G} I\)  for some constant \(0<\gamma _{G} \le 1\) .
Together with the conditions on \(B_t\) , we know that the Newton system (REF ) has a unique solution (cf. [1]}), and that the KKT matrix inverse \(K_t^{-1}\)  is uniformly bounded.
We denote by \(\Vert K_t^{-1}\Vert  \le \Upsilon _K\)  for \(\Upsilon _K \ge 1\) .
